Raising dimension under all projections
Cobb, John
Fundamenta Mathematicae, Tome 144 (1994), p. 119-128 / Harvested from The Polish Digital Mathematics Library
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As a special case of the general question - “What information can be obtained about the dimension of a subset of ℝn by looking at its orthogonal projections into hyperplanes?” - we construct a Cantor set in ℝ3 each of whose projections into 2-planes is 1-dimensional. We also consider projections of Cantor sets in ℝn whose images contain open sets, expanding on a result of Borsuk.

Publié le : 1994-01-01
EUDML-ID : urn:eudml:doc:212018 
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     author = {John Cobb},
     title = {Raising dimension under all projections},
     journal = {Fundamenta Mathematicae},
     volume = {144},
     year = {1994},
     pages = {119-128},
     zbl = {0821.54020},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-fmv144i2p119bwm}
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Cobb, John. Raising dimension under all projections. Fundamenta Mathematicae, Tome 144 (1994) pp. 119-128. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-fmv144i2p119bwm/

[00000] [B] K. Borsuk, An example of a simple arc in space whose projection in every plane has interior points, Fund. Math. 34 (1947), 272-277. | Zbl 0032.31404

[00001] [E] R. Engelking, Dimension Theory, PWN, Warszawa, and North-Holland, Amsterdam, 1978.

[00002] [M] S. Mardešić, Compact subsets of Rn and dimension of their projections, Proc. Amer. Math. Soc. 41 (2) (1973), 631-633. | Zbl 0272.54030

[00003] [R] Referee's comment